) 𝑃𝑄𝑅 is a right triangle, with the right angle at 𝑄. Based on the information that the perimeter of
Δ 𝑃𝑄𝑅 is 126 𝑐𝑚, and the area is 630 sq. cm, find the length of the hypotenuse (𝑃𝑅)

Let's solve this step-by-step.

1. **Define Variables:**
   - Let \( PQ = a \), \( QR = b \), and \( PR = c \) (hypotenuse of the triangle).
   
2. **Use Perimeter Information:**
   - The perimeter of \( \triangle PQR \) is given as 126 cm:
     \[
     a + b + c = 126
     \]

3. **Use Area Information:**
   - The area of \( \triangle PQR \) is given as 630 square cm. Since \( \triangle PQR \) is a right triangle with \( Q \) as the right angle, the area can be calculated as:
     \[
     \frac{1}{2} \cdot a \cdot b = 630
     \]
   - Multiplying both sides by 2, we get:
     \[
     a \cdot b = 1260
     \]

4. **Use Pythagoras' Theorem:**
   - In a right triangle, \( c^2 = a^2 + b^2 \).

5. **Express \( b \) in Terms of \( a \) and Substitute:**
   - From the perimeter equation, \( b = 126 - a - c \).
   - Using \( c^2 = a^2 + b^2 \) along with \( a \cdot b

𝑃𝑄𝑅 is a right triangle, with the right angle at 𝑄. Based on the information that the perimeter of Δ 𝑃𝑄𝑅 is 126 cm, and the area is 630 sq. cm, find the length of the hypotenuse (𝑃𝑅).

Explore how to find the hypotenuse of a right triangle with a given perimeter of 126 cm and area of 630 sq. cm. This problem covers essential geometry concepts, including the perimeter, area, and Pythagorean theorem, ideal for students in Grades 8-10.

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